2017 AMC 12B Problem 5

Question

The data set

[6, 19, 33, 33, 39,

41,

41,

43,

51,

57]

has median

Q_2 = 40,

first quartile

Q_1 = 33,

and third quartile

Q_3 = 43.

An outlier in a data set is a value that is more than

1.5

times the interquartile range below the first quartile

(Q_1)

or more than

1.5

times the interquartile range above the third quartile

(Q_3),

where the interquartile range is defined as

Q_3 - Q_1.

How many outliers does this data set have?

0

1

2

3

4

The interquartile range is

Q_3 - Q_1 = 43 - 33 = 10

Count values below

33 - 1.5(10)

or above

43 + 1.5(10)

The interquartile range is

43 - 33 = 10,

so

1.5

times it is

15.

Outliers are values less than

33 - 15 = 18

or greater than

43 + 15 = 58.

Only

6

falls below

18,

and nothing exceeds

58,

so there is exactly

1

outlier.

Thus, the correct answer is B.

Problem 5 in other years